Dynamical systems talk in Milano

Seminario Matematico e Fisico di Milano

Monday June 21, 5pm

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Speaker: Jacopo De Simoi (University of Toronto)

Title: Dynamical rigidity of convex billiards 

Abstract: Convex billiards are a classical topic in conservative dynamics. Typically, their dynamics is qualitatively very intricate, since it showcases a coexistence of hyperbolic dynamics and KAM phenomena. Understanding long-term statistical properties of the dynamics with the current technology is essentially an intractable problem. Here I venture in the opposite direction and I will discuss dynamical inverse problems: how much geometrical information can be extracted from the dynamics? More precisely: what can be deduced about the billiard table if one knows the lengths of all periodic orbits? The quantum version of this question has been famously stated as “Can one hear the shape of a drum?” In this talk I will review the latest results and describe the next steps in this direction. This is a joint project with Vadim Kaloshin.